Question

\(\frac{10}{56}+\frac{10}{140}+...+\frac{10}{1400}\)=?

Answer 1

\(=\frac{5}{28}+\frac{1}{14}+...+\frac{1}{140}=\frac{5}{4.7}+\frac{5}{7.10}+...+\frac{5}{25.28}\)

\(=\frac{5}{3}.\left(\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{25.28}\right)=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{25}-\frac{1}{28}\right)\)

\(=\frac{5}{3}.\left(\frac{1}{4}-\frac{1}{28}\right)=\frac{5}{3}.\left(\frac{7}{28}-\frac{1}{28}\right)=\frac{5}{3}.\frac{6}{28}=\frac{5}{14}\)